Archon

This page presents a topic of primarily mathematical interest. While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

Archon

Subgroups	2.3.5
Comma basis	5/4
Reduced mapping	⟨1; 1 0]
ET join	1 & 2c
Generators (CTE)	~3/2 = 702.0 ¢
MOS scales	1L 1s, 2L 1s, 2L 3s, 5L 2s
Ploidacot	monocot
Pergen	(P8, P5)
Minimax error	5-odd-limit: 386.3 ¢; 5-limit 15-odd-limit: 386.3 ¢
Target scale size	5-odd-limit: 3 notes; 5-limit 15-odd-limit: 5 notes

Archon is the 5-limit rank-2 temperament tempering out 5/4, the classical major third, such that the 5th harmonic is identified with a stack of two octaves. This temperament is clearly not meant for melodic or harmonic use due to its extreme inaccuracy. It could, however, serve as a skeleton where Pythagorean tuning is the base, and higher limits are built off of it directly using reduced harmonics like 5/4 rather than commas like 81/80, such as in Shasavistic theory.

The only patent val supporting it is that of 1edo.

For technical data see Very low accuracy temperaments #Archon.

See also

• Bixby, the 5-limit rank-2 temperament tempering out 4/3
• Seesaw, the 5-limit rank-2 temperament tempering out 6/5